With Saint-Etienne not playing Nice until Sunday, Bordeaux had the opportunity to put pressure on Christophe Galtier's side, but they were undone by a 66th-minute howler from Slovenian shot-stopper Jug.
Midfielder Jordan Veretout's 23rd-minute opener for Nantes had been cancelled out by Kian Hansen's own goal five minutes later, but Jug gifted the points to the hosts when he fumbled the ball over the line after a poor defensive clearance from Cheick Diabate.
Bordeaux were not the only top-six side to suffer defeat, with Rennes losing 2-0 at Bastia.
Rennes could have gone level with Bordeaux with a victory in Corsica but could not overcome a numerical disadvantage after defender Fallou Diagne was shown a straight red card midway through the first half.
Goals from Ryad Bodebouz and Yannick Cahuzac sealed a victory for the islanders that puts them within a point of moving out of the bottom three.
Lorient put distance between themselves and the relegation places by beating Metz 3-1, while second-bottom Lens claimed a valuable point in a 3-3 draw at Montpellier.
Anthony Mounier looked to have given the hosts the points with a 63rd-minute effort after Montpellier had previously squandered a two-goal lead, only for Yoann Touzghar to salvage a share of the spoils with his fourth goal of the season 10 minutes from time.
There was similar drama at the Stade Auguste Delaune as Reims overcame Evian 3-2.
Daniel Wass and Cedric Cambon were on target to put Evian 2-1 ahead, but the contest turned in the 78th minute when Algeria defender Aissa Mandi equalised.
Cambon was sent off in the aftermath for dissent and the hosts duly took advantage, Brazilian forward Diego hitting home his second of the game two minutes later to complete the turnaround.